有粘结预应力混凝土简支梁动力有限元程序设计

Dynamic Finite Element Programing of Simply Supported Bonded Prestressed Concrete Beams

本文对有粘结预应力混凝土简支梁进行动力有限元程序设计。用平面四边形等参单元模拟混凝土单元,将钢筋分布到混凝土单元中;混凝土和钢筋均采用线弹性本构关系;力筋预应力对梁刚度和频率的影响,参考有关文献方法来修正刚度矩阵;特征值问题的解法,考虑标准特征值和广义特征值问题的各种算法,并考虑集中质量矩阵和一致质量矩阵对计算结果的影响,采用广义雅克比法和子空间迭代法解广义特征值问题。最后,针对试验,运用所编程序进行分析计算,将计算结果与试验结果进行对比,本文所编程序在简支梁动力有限元分析中的固有模态计算问题上具有相对较高的精度。

The dynamic finite element program of bonded prestressed concrete beams was designed. The concrete element was simulated by quadrilateral isoperimetric element. And the steels were distributed to concrete. The linear elastic constitutive relationship was used. The contribulion of prestressed force of steel was considered as amendment to stiffness matrix according to the correlation documentation. The generalized Jacobi method and subspace interaction method were used to solve the eigenvalue problem. The algorithm of generalized eigenvalue problem and standard eigenvalue problem were considered. And the contribution of lumped mass matrices and uniform mass matrices were considered. At last, based on the experiment of three bonded prestressed concrete simple supported beams, the natural frequency of the beam was calculated by the program. Comparing with the experimental results, the precision of the program is verified.